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PubMed2005

Protein-surface interactions: an energy-based mathematical model.

This article describes an energy-based approach to protein adsorption, focusing on the energies involved in the interactions between a protein and a surface. Mathematical modeling and simulation based on this approach allow an improved understanding of the conditions that favor or prevent adsorption of a protein onto a surface and that can play a significant role in the design of material surfaces that interact with biological tissues according to specific needs. Biocompatibility with respect to fluids in motion, such as blood, is the main foreseeable application of our work. The considered energies are the van der Waals energy, the electrostatic energy, and the hydrophobic or hydrophilic energy. Moreover, the motion of the medium in which particles are immersed is also taken into account, considering the drag effect of the motion of the fluid on the particle, leading to a kinetic contribution to the total energy. It is shown that the adsorption behavior is not mainly determined by the van der Waals energy and by the double layer energy, but that a significant role is also played by the hydrophobic or hydrophilic energy. These results support the findings of experimental studies.

Adsorption↗
PubMed1998

[A human knee articulate mathematical model on femur-tibia-patella 3-segmetents].

In this paper, based on the previous work of S. Turgut Tumer et al, a human knee articulate mathematical model on femur-tibia-patella 3-segments is established by introducing patella-femur joint. This model includes both rolling and slipping motions of femur-tibia joint and femur-patella joint. It can be employed in simulating the biodynamic response of human lower extremity.

Biomechanical Phenomena↗
PubMed2003

[Mathematical modeling in gerontology--strategic perspectives].

Mathematical description of aging and mortality is presented. A review of tendencies in modeling is discussed and some difficulties related to adequacy and the ways of information presentation in the models are talked about. A short view is given at the two main modeling techniques in biology, namely the models of data and models of a system. Strategic perspectives of modeling in biogerontology are presented in terms of modeling paradigms. One can speak about a general paradigm consisting of postulates, principles and techniques related to a model, which allows a solving different problems with the same model, if the model can be modified to treat the variety of problems. Modification is to be done in the framework of concepts of the model by using a sum of the methods related to it. It is shown how the homeostatic paradigm can be used to predict a specific human longevity.

Aging↗
PubMed1991

A mathematical model for Plasmodium vivax malaria transmission: estimation of the impact of transmission-blocking immunity in an endemic area.

We have developed a multi-state mathematical model to describe the transmission of Plasmodium vivax malaria; the model accommodates variable transmission-blocking/enhancing immunity during the course of a blood infection, a short memory for boosting immunity, and relapses. Using the model, we simulated the incidence of human malaria, sporozoite rates in the vector population, and the level of transmission-blocking immunity for the infected population over a period of time. Field data from an epidemiological study conducted in Kataragama in the south of Sri Lanka were used to test the results obtained. The incidence of malaria during the study period was simulated satisfactorily. The impact of naturally-acquired transmission-blocking immunity on malaria transmission under different vectorial capacities was also simulated. The results show that at low vectorial capacities, e.g., just above the threshold for transmission, the effect of transmission-blocking immunity is very significant; however, the effect is lower at higher vectorial capacities.

Animals↗
PubMed1974

A critical review of the field application of a mathematical model of malaria eradication.

A malaria control field research trial in northern Nigeria was planned with the aid of a computer simulation based on Macdonald's mathematical model of malaria epidemiology. Antimalaria attack was based on a combination of mass drug administration (chloroquine and pyrimethamine) and DDT house spraying. The observed results were at great variance with the predictions of the model. The causes of these discrepancies included inadequate estimation of the model's basic variables, and overestimation, in planning the simulation, of the effects of the attack measures and of the degree of perfection attainable by their application. The discrepancies were to a great extent also due to deficiencies in the model. An analysis is made of those considered to be the most important. It is concluded that research efforts should be encouraged to increase our knowledge of the basic epidemiological factors, their variation and correlations, and to formulate more realistic and useful theoretical models.

Animals↗
PubMed2001

From cell death to embryo arrest: mathematical models of human preimplantation embryo development.

Human preimplantation embryos exhibit high levels of apoptotic cells and high rates of developmental arrest during the first week in vitro. The relation between the two is unclear and difficult to determine by conventional experimental approaches, partly because of limited numbers of embryos. We apply a mixture of experiment and mathematical modeling to show that observed levels of cell death can be reconciled with the high levels of embryo arrest seen in the human only if the developmental competence of embryos is already established at the zygote stage, and environmental factors merely modulate this. This suggests that research on improving in vitro fertilization success rates should move from its current concentration on optimizing culture media to focus more on the generation of a healthy zygote and on understanding the mechanisms that cause chromosomal and other abnormalities during early cleavage stages.

Apoptosis↗
PubMed2005

Mathematical model--tell us the future!

Studying bacterial resistance has direct importance for the antimicrobial treatment of individual patients. In addition, surveillance data pooled from individual diagnostic reports help physicians to choose the most effective drug for empirical therapy. However, this is not the limit of what can be done with the resistance data. There is an increasing need to synthesize the available strands of data in order to construct mathematical models that can be used as tools to predict the likely outcomes of various antibiotic policy options.

Anti-Bacterial Agents↗
PubMed1990

Mathematical models of gene amplification with applications to cellular drug resistance and tumorigenicity.

An increased number of copies of specific genes may offer an advantage to cells when they grow in restrictive conditions such as in the presence of toxic drugs, or in a tumor. Three mathematical models of gene amplification and deamplification are proposed to describe the kinetics of unstable phenotypes of cells with amplified genes. The models differ in details but all assume probabilistic mechanisms of increase and decrease in gene copy number per cell (gene amplification/deamplification). Analysis of the models indicates that a stable distribution of numbers of copies of genes per cell, observed experimentally, exists only if the probability of deamplification exceeds the probability of amplification. The models are fitted to published data on the loss of methotrexate resistance in cultured cell lines, due to the loss of amplified dihydrofolate reductase gene. For two mouse cell lines unstably resistant to methotrexate the probabilities of amplification and deamplification of the dihydrofolate reductase gene on double minute chromosomes are estimated to be approximately 2% and 10%, respectively. These probabilities are much higher than widely presumed. The models explain the gradual disappearance of the resistant phenotype when selective pressure is withdrawn, by postulating that the rate of deamplification exceeds the rate of amplification. Thus it is not necessary to invoke a growth advantage of nonresistant cells which has been the standard explanation. For another analogous process, the loss of double minute chromosomes containing the myc oncogene from SEWA tumor cells, the growth advantage model does seem to be superior to the amplification and deamplification model. In a more theoretical section of the paper, it is demonstrated that gene amplification/deamplification can result in reduction to homozygosity, such as is observed in some tumors. Other applications are discussed.

Animals↗
PubMed1996

Mathematical modelling, simulation and prediction of tumour-induced angiogenesis.

Angiogenesis, the formation of blood vessels from a pre-existing vasculature, is a process whereby capillary sprouts are formed in response to externally supplied chemical stimuli. The sprouts then grow and develop, driven by endothelial cell migration and proliferation, and organise themselves into a dendritic structure. Angiogenesis occurs during embryogenesis, wound healing, arthritis and during the growth of solid tumours. In this paper we present a novel mathematical model which describes the formation of the capillary sprout network in response to chemical stimuli (tumour angiogenesis factors, TAF) supplied by a solid tumour. The model also takes into account endothelial cell-extracellular matrix interactions via the inclusion of fibronectin in the model. The model consists of a system of nonlinear partial differential equations describing the response in space and time of endothelial cells to the TAF and the fibronectin (migration, proliferation, anastomosis, branching). Using the discretized system of partial differential equations, we use a deterministic cellular automata (DCA) model, which enables us to track individual endothelial cells and incorporate branching explicity into the model. Numerical simulations are presented which are in very good qualitative agreement with experimental observations. Certain experiments are suggested which could be used to test the hypotheses of the model and various extensions and developments of the model with particular applications to anti-angiogenesis strategies are discussed.

Animals↗
PubMed1995

Intracranial pressure dynamics in patients with acute brain damage: a critical analysis with the aid of a mathematical model.

The time pattern of intracranial pressure (ICP) in response to typical clinical tests (i.e., bolus injection and bolus withdrawal of 1 to 4 mL of saline in the craniospinal space) was studied in 18 patients with acute brain damage by means of a mathematical model. The model includes the main biomechanical factors assumed to affect intracranial pressure, particularly cerebrospinal fluid (CSF) dynamics, intracranial compliance, and cerebral hemodynamics. Best fitting between model simulation curves and clinical tracings was achieved using the Powell minimization algorithm and a least-square criterion function. The simulation results demonstrate that, in most patients, the ICP time pattern cannot be explained merely on the basis of CSF dynamics but also requires consideration of the contribution of cerebral hemodynamics and blood volume alterations. In particular, only in a few patients (about 40% of total) the ICP monotonically returns toward baseline following the clinical maneuver. In most of the examined cases (about 60%), ICP exhibits an anomalous response to the same maneuver, characterized by a delayed increase after bolus injection and a delayed decrease after withdrawal. The model is able to explain these responses, imputing them to active intracranial blood volume changes induced by mechanisms controlling cerebral blood flow. Finally, the role of the main intracranial biomechanical parameters in the genesis of the ICP time pattern is discussed and a comparison with previous theoretical studies performed.

Acute Disease↗
PubMed1985

Mathematical model of muscular fatigue. II. Changes of metabolites level and of force during exercise in relation to a fatigability parameter.

In order to study muscular fatigue, a mathematical model allowing the simulation of changes of metabolites level and of force during exercise in human muscle is built. It results from the association of two previous models and from the introduction of two parameters (pH and ATP concentration) influencing directly the muscular force and of the fatigability parameter (A) which characterizes the oxidative capacity of a given fibre. Simulations of physiological conditions of exercise and recovery allow one to bring out a classification of muscular fibres in terms of the fatigability parameter. In addition, the study of successive exercises underlines the lactate level role in force generation. Computations have been carried out on a computer DPS 7.

Adenosine Triphosphate↗
PubMed2006

Mathematical model of mitochondrial ionic homeostasis: three modes of Ca2+ transport.

Mitochondria play an important role in regulation of Ca2+ homeostasis in a cell. Here we present a mathematical model of mitochondrial ion transport and use this model to analyse different modes of Ca2+ uptake by mitochondria. The model includes transport of H+, Ca2+, K+, inorganic phosphate and oxidative substrates across the inner mitochondrial membrane harboring permeability transition pore (PTP). The detailed description of ion fluxes is based on the experimental ion kinetics in isolated mitochondria. Using the model we show that the kinetics of Ca2+ uptake by mitochondria is regulated by the total amount of Ca2+ in the system and the rate of Ca2+ infusion. Varying these parameters we find three different modes of ion transport. When the total amount of Ca2+ is below 140 nmol Ca2+/mg protein, all available Ca2+ is accumulated in the matrix without activation of the PTP. Between 140 and 160 nmol Ca2+/mg protein, accumulation of Ca2+ generates periodic opening and closure of the PTP and oscillations of ion fluxes. Higher levels of Ca2+ (> 160 nmol Ca2+/mg protein) result in a permanently open PTP, membrane depolarization and loss of small ions from the matrix. We show that in the intermediate range of Ca2+ concentrations the rate of Ca2+ infusion regulates the PTP state, so that slow Ca2+ infusion does not lead to PTP opening, while fast Ca2+ infusion results in an oscillatory state.

Animals↗
PubMed2003

Acyclovir permeation through rat skin: mathematical modelling and in vitro experiments.

The aim of this work is to characterise the skin permeation properties of a male rat by means of a purely diffusive mathematical model based on Fick's second law. Additionally, in the attempt of proposing a reliable tool allowing the skin permeability (or resistance) determination on the basis of experimental data, the model automatically accounts also for two typical experimental conditions. In particular, drug dissolution in the donor environment and receiver sampling technique (part of the receiver volume is withdrawn and immediately replaced by fresh solvent) are considered. The results of this characterisation are then compared with those coming from a common simplified approach. Acyclovir is chosen as model drug and a thermostatic (37 degrees C) Franz cell apparatus is used to perform permeation experiments. This study suggests that Acyclovir permeation through the rat skin can be well described by the proposed model and that some differences arise in the evaluation of the full-skin resistance performed by means of our model or the usual simpler approach.

Acyclovir↗
PubMed2000

Hydrophilic matrices for controlled drug delivery: an improved mathematical model to predict the resulting drug release kinetics (the "sequential layer" model).

PURPOSE: The aims of this study were (i) to elucidate the transport mechanisms involved in drug release from hydrophilic matrices; and (ii) to develop an improved mathematical model allowing quantitative predictions of the resulting release kinetics. METHODS: Our previously presented model has been substantially modified, by adding: (i) inhomogeneous swelling; (ii) poorly water-soluble drugs; and (iii) high initial drug loadings. The validity of the improved model has been tested experimentally using hydroxypropyl methylcellulose (HPMC)-matrices, containing either a poorly or a freely water-soluble drug (theophylline or chlorpheniramine maleate) at various initial loadings in phosphate buffer pH 7.4 and 0.1 N HCl, respectively. RESULTS: By overcoming the assumption of homogeneous swelling we show that the agreement between theory and experiment could be significantly improved. Among others, the model could describe quantitatively even the very complex effect on the resulting relative release rates (first slowing down, then accelerating drug release) observed when increasing the initial loading of poorly water-soluble drugs. CONCLUSIONS: The practical benefit of this work is an improved design model that can be used to predict accurately the required composition and dimensions of drug-loaded hydrophilic matrices in order to achieve desired release profiles, thus facilitating the development of new pharmaceutical products.

Chemistry, Pharmaceutical↗
PubMed1989

Mathematical model for addiction: application to multiple risk factor intervention trial data for smoking.

Describes habituation and addiction, both psychological and physiological, using the simple equations of the mathematical model of ideodynamics. The parameters in these equations were optimized to smoking data from the Multiple Risk Factor Intervention Trial (MRFIT) program. With only 4 constant parameters, it was possible to calculate accurate time trends for recidivism to smoking among quitters, time trends for secondary cessation among recidivists, and final percentage of smokers in a population with both recidivism and secondary cessation occurring simultaneously. These same parameters further permit predictions for the long-range success of intervention programs to decrease substance dependency. Ideodynamics can also predict time trends of public opinion based on stories in the mass media.

Behavior Therapy↗
PubMed2000

Indications for limited echocardiographic imaging: a mathematical model.

BACKGROUND: Few data exist on the magnitude of potential time savings obtained by using a limited echocardiographic (echo) imaging strategy on a referral population. METHODS: A mathematical model of a limited echo screening strategy was devised that used as variables the length of the limited examination and the probability of detecting the referral diagnosis or a significant incidental finding, and assumed that any abnormality would mandate a full study. Data from prior echo population studies were used in the model as examples. RESULTS: The model demonstrated a direct relation in time savings for populations with a low prevalence of disease and incidental findings. The model predicted that a limited echo imaging strategy could result in significant time savings when applied to certain specific referral populations. CONCLUSIONS: The time savings of a limited echo screening strategy can be modeled as a function of the length of the limited screen and the presence of significant findings. This model may provide the framework in which future prospective studies can confirm indications for limited echo.

Cardiovascular Diseases↗
PubMed2000

Comparison of mathematical models for exposure assessment with computational fluid dynamic simulation.

For many years exposure to airborne contaminants has been estimated by air or biological monitoring. In occupational settings, mathematical models increasingly are employed as adjuncts to monitoring, for instance, during process design or in retrospective epidemiological studies. Models can make predictions in a wide variety of scenarios, can be used for rapid screening, and may reduce the need for monitoring in exposure assessment. However, models make simplifying assumptions regarding air flow and contaminant transport. The errors resulting from these assumptions have not been systematically evaluated. Here we compare exposure estimates from the single-zone completely mixed (CM-1), two-zone completely mixed (CM-2), and uniform diffusivity (UD) models with workroom concentration fields predicted by computational fluid dynamics (CFD). The room air flow, concentration fields, and the breathing zone concentration of a stationary worker were computed using Fluent V4.3 for factorial combinations of three source locations, three dilution air flow rates and two emission rate profiles, constant and time-varying. These numerical experiments were used to generate plausible concentration fields, not to simulate exactly the processes in a real workroom. Thus, "error" is defined here as difference between model and CFD predictions. For both constant and time-varying emission sources, exposure estimates depended on receptor and source location. For the constant source case, ventilation rate was shown to be inconsequential to CM-1 model error. CM-1, CM-2, and UD models differed in their agreement with CFD. UD was closest to CFD for estimating concentration in the simulated breathing zone (BZ) near the source, although large errors resulted when the model was applied to the plane of possible breathing zones. CM-1 performed better for this plane but underestimated the near-source BZ exposure. For the near-source BZ location, CM-2 replicated CFD predictions more closely than CM-1 did, but less closely than UD did. Error in CM-1 model estimation of short-term average exposure to a time-varying source was highly dependent on ventilation rate. Error decreased as ventilation rate increased.

Air Movements↗
PubMed1997

A simple mathematical model and practical approach for evaluating citric acid cycle fluxes in perfused rat hearts by 13C-NMR and 1H-NMR spectroscopy.

We propose a simple mathematical model and a practical approach for evaluating the flux constant and the absolute value of flux in the citric acid cycle in perfused organs by 13C-NMR and 1H-NMR spectroscopy. We demonstrate that 13C-NMR glutamate spectra are independent of the relative sizes of the mitochondrial and cytosolic compartments and the exchange rates of glutamates, unless there is a difference in 13C chemical shifts of glutamate carbons between the two compartments. Wistar rat hearts (five beating and four KCl-arrested hearts) were aerobically perfused with 100% enriched [2-(13)C]acetate and the kinetics of glutamate carbon labeling from perchloric acid extracts were studied at various perfusion times. Under our experimental conditions, the citric acid cycle flux constant, which represents the fraction of glutamate in exchange with the citric acid cycle per unit time, is about 0.350 +/- 0.003 min(-1) for beating hearts and 0.0741 +/- 0.004 min(-1) for KCl-arrested hearts. The absolute values of the citric acid flux for beating hearts and for KCl-arrested hearts are 1.06 +/- 0.06 micromol x min(-1) x mg(-1) and 0.21 +/- 0.02 micromol x min(-1) x g(-1), respectively. The fraction of unlabeled acetate determined from the proton signal of the methyl group is small and essentially the same in beating and arrested hearts (7.4 +/- 1.7% and 8.8 +/- 2.1%, respectively). Thus, the large difference in the Glu C2/C4 between beating and arrested hearts is not due to the important contribution from anaplerotic sources in arrested hearts but simply to a substantial difference in citric acid cycle fluxes. Our model fits the experimental data well, indicating a fast exchange between 2-oxoglutarate and glutamate in the mitochondria of rat hearts. Analysis of the flux constant, calculated from the half-time of glutamate C4 labeling given in the literature, allows for a comparison of the citric acid flux for various working conditions in different animal species.

Acetic Acid↗